"Whether it came from Russia, with the Russian government's knowledge, is not known to me at this point," Tillerson said. He said it's almost "beyond comprehension" that an organized state would take the dangerous substance to another country and public place where others could get hurt.

Tillerson said he's become "extremely concerned about Russia" despite what he said was a year of trying to work with the country. "Instead what we've seen is a pivot on their part to be more aggressive," he said.

In a separate statement, the State Department said, "Russia continues to be an irresponsible force of instability in the world, acting with open disregard for the sovereignty of other states and the life of their citizens." It added that those who committed the crime "must face appropriately serious consequences."

Earlier Monday, White House press secretary called the attack "reckless, indiscriminate and irresponsible," but stopped short of agreeing with May that Russia was likely behind the poisoning.